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Permutation-based inference for functional data in process optimization

  • Elena Barzizza
  • Nicolò Biasetton
  • Alessandro Fanesi
  • Pietro Di Gioia
  • Luca Anghileri
  • Alberto Dolci
  • Luigi Salmaso

In a food processing context, the temperature at the end of a defrosting process plays a critical role in ensuring product quality and production efficiency. Excessively high temperatures risk compromising product integrity, while low temperatures can delay subsequent processing steps. In collaboration with an industrial partner, a Design of Experiments (DoE) was conducted to identify the optimal configuration of a defrosting system, with the goal of achieving a target final temperature that facilitates smooth transition to the next production phase and minimizes downtime. Temperature measurements were collected using multiple sensors throughout the defrosting cycle, recorded at regular intervals—resulting in data naturally represented as functions over time. This study illustrates the effectiveness and practical applicability of permutation-based statistical inference using the NonParametric Combination (NPC) methodology for the analysis of functional data. Emphasizing the functional nature of the data avoids the loss of information typically associated with the extraction of arbitrary summary features, highlighting the value of functional approaches in industrial experimentation.

  • Keywords:
  • Functional data,
  • NPC,
  • Permutation methods,
  • Design of Experiment,
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Elena Barzizza

University of Padua, Italy - ORCID: 0000-0002-6389-887X

Nicolò Biasetton

University of Padua, Italy - ORCID: 0000-0002-1123-9899

Alessandro Fanesi

University of Padua, Italy - ORCID: 0009-0002-3789-0513

Pietro Di Gioia

Bolton Food S.p.A., Italy

Luca Anghileri

Bolton Food S.p.A., Italy

Alberto Dolci

Bolton Food S.p.A., Italy

Luigi Salmaso

University of Padua, Italy - ORCID: 0000-0001-6501-1585

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  2. Corain, L., Melas, V.B., Pepelyshev, A., Salmaso, L. (2014). New insights on permutation approach for hypothesis testing on functional data. Advances in Data Analysis and Classification, 8(3), pp. 339- 356.
  3. Cox, D.D., Lee J.S. (2008). Pointwise testing with functional data using the Westfall-Young randomization method. Biometrika, 95(3), pp. 621-634.
  4. Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2), pp. 65-70.
  5. Pesarin, F., Salmaso, L. (2025). Permutation Tests for Complex Data: Theory, Applications and Software. 2nd. Chichester, UK: Wiley Series in Probability.
  6. Pini, A., Vantini, S. (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics (Taylor \& Francis), 29(2), pp. 407-424.
  7. Ramsay, J., Hooker G., Graves, S. (2009). Functional Data Analysis with R and MATLAB. New York, NY: Springer.
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  • Publication Year: 2026
  • Pages: 51-56
  • Content License: CC BY 4.0
  • © 2026 Author(s)

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  • Publication Year: 2026
  • Content License: CC BY 4.0
  • © 2026 Author(s)

Chapter Information

Chapter Title

Permutation-based inference for functional data in process optimization

Authors

Elena Barzizza, Nicolò Biasetton, Alessandro Fanesi, Pietro Di Gioia, Luca Anghileri, Alberto Dolci, Luigi Salmaso

Language

English

DOI

10.36253/979-12-215-1062-1.11

Peer Reviewed

Publication Year

2026

Copyright Information

© 2026 Author(s)

Content License

CC BY 4.0

Metadata License

CC0 1.0

Bibliographic Information

Book Title

Data, Statistics and AI for Well-Being of People and Organisations

Editors

Luigi Fabbris, Alberto Franci, Pietro Renzi

Peer Reviewed

Number of Pages

420

Publication Year

2026

Copyright Information

© 2026 Author(s)

Content License

CC BY 4.0

Metadata License

CC0 1.0

Publisher Name

Firenze University Press

DOI

10.36253/979-12-215-1062-1

ISBN Print

979-12-215-1061-4

eISBN (pdf)

979-12-215-1062-1

eISBN (xml)

979-12-215-1063-8

Series Title

Applied Statistics Series

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